Impact of stoichiometry and strain on Ge_1-x Sn_x alloys from first principles calculations

We calculate the electronic structure of germanium-tin (Ge1-x Sn x ) binary alloys for 0 ≤ x ≤ 1 using density functional theory (DFT). Relaxed alloys with semiconducting or semimetallic behaviour as a function of Sn composition x are identified, and the impact of epitaxial strain is investigated by constraining supercell lattice constants perpendicular to the [001] growth direction to the lattice constants of Ge, zinc telluride, or cadmium telluride substrates. It is found that application of 1% tensile strain reduces the Sn composition required to bring the (positive) direct band gap to zero by approximately 5% compared to a relaxed Ge1-x Sn x alloy having the same gap at Γ. On the other hand, compressive strain has comparatively less impact on the alloy band gap at Γ. Using DFT calculated alloy lattice and elastic constants, the critical thickness for Ge1-x Sn x thin films as a function of x and substrate lattice constant is estimated, and validated against supercell DFT calculations and experiment. The analysis correctly predicts the Sn composition range at which it becomes energetically favourable for Ge1-x Sn x /Ge to become amorphous. The influence of stoichiometry and strain is examined in relation to reducing the magnitude of the inverted ('negative') Γ7-Γ8+ band gap, which is characteristic of semimetallic alloy electronic structure. Based on our findings, strategies for engineering the semimetal-to-semiconductor transition via strain and quantum confinement in Ge1-x Sn x nanostructures are proposed.